I have the same problem, I am unable to install the Adobe Air Installer and get the "admin permission" error. I installed and ran the FixIt but it found no problems. When I look in my control panel under the programs to uninstall (thinking if I uninstall the current version of Adobe Air I could try to reinstall it) there is no Adobe Air program, just the Adobe Reader.
I'm not sure where to go with this now. I would greatly appreciate some help with this as I continually get error messages about not having Adobe Air installed and certain programs won't work without it.